Section 7.6 Cars. Understanding a fixed installment loan.

Transcription

1 184 Section 7.6 Cas Objective #1: Undestanding a fixed installment loan. An installment loan is a loan that is paid off in weekly o monthly payments. If the weekly o monthly payments ae the same, then the loan is called a fixed installment loan. A potion of each payment goes to pay fo the inteest and the est goes to pay down the pincipal. As moe payments ae made, less of the payment goes to the inteest and moe towads the pincipal. Many people will use a fixed installment loan to puchase an item that they do not have the money to buy outight such as a house, a ca, o a college education. In annuities, as a peson makes peiodic deposits, the account will ean moe and moe inteest. In this case, the inteest is woking with the peson making the deposits. With installment loans, the inteest is woking against the boowe since each payment has to fist payoff the inteest on the loan, befoe the emainde can be applied to pincipal. Theefoe, when compaed to the annuity fomula fo the peiodic deposit, the tems in the denominato with have opposite signs and the exponent of the (1 + /n facto will be negative. Loan Payment fo a fixed installment loan Let P be the amount of the fixed installment loan whee egula payments ae made n times a yea fo t yeas at an annual inteest ate (as a decimal. The egula payment PMT equied to epay the loan is given by: PMT P( n n nt Solve the following: Ex. 1 A custome has a choice of two ca loans to finance the puchase of $20,000 ca. The cedit union offes a thee-yea loan at 6.65% while the dealeship offes a five-yea loan at 7.15%. Find the monthly payment and the total inteest fo each loan and compae. Fo the cedit union, plug P 20000, , n, & t 3 into: P( n 20000( PMT n nt

2 ( [1 ( $ Total inteest 36( $ Fo the dealeship, plug P 20000, , n, & t 5 into: P( n 20000( PMT n nt ( [1 ( $ Total inteest 60( $ With the dealeship loan, the monthly payment is smalle by ove $200, but the peson will have to pay it fo two additional yeas and will pay almost twice as much in inteest. Objective #2: Undestanding leasing a ca Instead of buying a ca, a consume has the option to leasing a ca. Leasing a ca is essential a long-tem ental ageement. With leasing a ca, esidual value, the estimated value of the ca at the end of the lease, becomes an impotant facto. Although ca leases ae vey complicated, thee ae essential two diffeent types of leasing ageements. Type 1: A closed-end lease is when a peson makes a fixed payment based upon the estimated use of the vehicle. At the end of the lease when the ca is etuned, the custome has to pay fo mileage in excess of the estimated use on the lease. Type 2: An open-end lease is when a peson makes a fixed payment based upon the ca's esidual value. At the end of the lease, the custome makes payment on the diffeence between the esidual value and the actual appaised value if the appaised value is lowe than the esidual value. Othewise, the custome owes nothing o may even eceive a efund. Advantages of leasing 1 The monthly lease payments ae usually much lowe than the monthly payments fo buying a new ca. The consume can theefoe lease a moe expensive ca than he o she could buy.

3 2 Often, little o no down payment is equied when leasing. 3 At the end of the lease, the consume etuns the ca to the dealeship and does not have to woy about selling the ca. 4 The peson who leases is always diving a late-model ca that is still unde the manufactue's waanty. Disadvantages of leasing 1 The custome does not own the ca at the end of the lease. 2 The finance chages ae typically highe fo leasing a ca so the custome pays moe than the equivalent loan amount fo a ca puchase. 3 The ca must be maintained in pistine condition. Any dent, dings, o othe damage will be costly at the end of the lease. 4 Lease contacts limit the numbe of mile diven to,000 to 15,000 miles pe yea. Any mileage above that will cost the custome between 10 to 25 pe mile. Howeve, thee is no cedit fo unused mileage. 5 If a peson ends a lease ealy, thee ae high temination fees and penalties that have to be paid. 6 A peson cannot customize the ca in any pemanent way. 7 When mileage and othe expenses ae taken into account at the end of the lease, the cost is typically highe than financing a ca. Objective #3: Undestanding the diffeent types of insuance. Ca insuance is anothe impotant component to owning o leasing a ca. Insuance potects against unexpected loss. Thee ae two types of ca insuance. 186 Type 1: Liability insuance is equied in just about evey state. This insuance potects against damage a dive does to othe people while opeating the vehicle. Thee ae two components to liability: Bodily injuy liability coves the expenses of a lawsuit if someone is injued o killed in an accident whee the dive is at fault. Popety damage liability coves damage to othe people's popety including othe cas fom the negligent opeation of the vehicle. Again, this type of insuance is NOT optional in most states.

4 187 Type 2: Collision and compehensive insuance is "optional" in most states. If a peson is financing o leasing a vehicle, then it is equied by the financing institution. This insuance potects against damage to the vehicle itself. Thee ae two components to collision and compehensive: Collision coveage pays fo the damage o loss of the vehicle in an accident whee the dive is at fault o the othe dive did not have insuance. Compehensive coveage pays fo damage o loss of the vehicle due to things like fie, theft, acts of natue, etc. Objective #4: Buying new vesus used. Most of the ca's depeciation occus in the fist couple yeas of owneship. Just diving a new ca off of a ca lot can depeciate it's value by a couple of thousands of dollas. Sometimes, buying a two o thee yea old vehicle can be a vey attactive altenative. Conside the cost of two cas in the next example whose pices wee fom Kelly Blue Book ( Solve the following Ex. 2 A custome is choosing between two cas to puchase. One is a band new Fod Fusion costing $23,100 and the othe is a thee-yea old Fod Fusion (38,000 miles on it costing $15,900. Eithe one can be financed with a fou-yea loan at 6.25%. What is the diffeence between the monthly payments? Fo the new Fusion, plug P $23100, , n, & t 4 into: P( n 23100( PMT n nt ( [1 ( $ Fo the used Fusion, plug P $15900, , n, & t 4 into: P( n 15900( PMT n nt ( [1 ( $ The diffeence is the monthly payment is $ o about $170.

5 188 Objective #5 Cost of owneship Aside fom the puchase pice, thee ae many othe cost associated with owning a ca including fuel, maintenance, epais, ties, tolls, insuance, license fees, egistation, and inspections. Of these costs, fuel accounts fo a lage potion of the cost. The fuel cost pe yea can be calculated multiplying the numbe a gallons used time the aveage pice pe gallon. Since the numbe of gallons used is equal to the annual miles diven divided by the miles pe gallon the ca gets, we can use the following fomula to calculate the annual cost of fuel: Cost of gasoline: Annual fuel expense annual miles diven miles pe gallon x Solve the following: Ex. 3 A sales epesentative dives 15,000 miles a yea fo wok. She has a choice of two cas to use, one getting 35 mpg and the othe getting 15 mpg. If gasoline aveages $3 pe gallon, a How much does she save pe yea in fuel expenses diving the moe fuel efficient vehicle? b If she wee to invest he monthly fuel savings into account paying 7.5% inteest compounded monthly, how much will she have saved afte 5 yeas? a Fist vehicle: 35 mpg Annual fuel expense x $3 $85.71 Second vehicle: 15 mpg Annual fuel expense x $3 $3000 pice pe gallon annual miles diven miles pe gallon x annual miles diven miles pe gallon x pice pe gallon pice pe gallon The savings pe yea is $

6 Ex. 4 b The monthly savings is $ / months $ Plugging P m $142.86, 0.075, t 5, and n into the fomula, we get: P m[(1 + n nt [( ( n ( [( [ He account will be woth $ Cindy is tying to choose between buying a egula Honda Accod and a Hybid Honda Accod. The egula Honda Accod gets 30 mpg and costs $24,200 while the Hybid Honda Accod gets 48 mpg and costs $30,500. How many miles must she dive the Hybid Honda Accod until the savings in fuel expenses offset the highe cost of the ca? Assume gasoline aveages $3 pe gallon. The diffeence in pice is $30,500 $24,200 $6,300. Let d miles diven Hybid: Fuel Expense d 48 (3 d Regula: Fuel Expense d (3 d 10 Regula Fuel Expense Hybid Fuel Expense d 10 d (multiply both sides by 80 8d 5d (subtact 5d fom both sides 3d (divide both sides by 3 d Veify the esults: Hybid Fuel expense Regula Fuel expense the hybid. A 30 x3 $10,500 x3 $16,800 which $6300 moe than Thus, she will need to dive the Hybid 168,000 miles befoe the highe cost of the Hybid is offset by the fuel savings. With cas, it is geneally ecommended that value of all the vehicles a peson owns should not exceed half of his o he annual income.